Math Meth Oper Res (2012) 75:29–65
DOI 10.1007/s00186-011-0374-1
ORIGINAL ARTICLE
Integrating inventory control and a price change
in the presence of reference price effects: a two-period
model
Alfred Taudes · Christian Rudloff
Received: 14 January 2011 / Accepted: 2 November 2011 / Published online: 17 November 2011
© Springer-Verlag 2011
Abstract Demand and procurement planning for consumer electronics products
must cope with short life cycles, limited replenishment opportunities and a willing-
ness to pay that is influenced by past prices and decreases over time. We therefore
propose the use of an integrated pricing and inventory control model with a two-period
linear demand model, in which demand also depends on the difference between a price-
history-based reference price and the current price. For this model we prove that the
optimal joint pricing/inventory policy for the replenishment opportunity after the first
period is a base-stock list-price policy. That is, stock is either replenished up to a
base-stock level and a list-price is charged, or it is not replenished and a discount is
given that increases with the stock-level. Furthermore, we use real-world cell phone
data to study the differences between an integrated policy and traditional sequential
optimization, where prices are initially optimized based on the expected demand and
ordering cost, and the resulting demand distribution is used to determine an optimal
inventory policy. Finally, we discuss possible extensions of the model.
Keywords Dynamic programming · Inventory control · Dynamic pricing ·
Reference price
A. Taudes (B )
Institute for Production Management, Vienna University for Economics and Business Administration,
Nordbergstrasse 15/3.St./A, 1090 Vienna, Austria
e-mail: Alfred.Taudes@wu.ac.at
C. Rudloff
Austrian Institute of Technology, Giefinggasse 2, 1210 Vienna, Austria
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